Sediment Growth and Aging as Markov Chains

Preservation of sediments as a function of their geologic age can be described by stochastic models for the following cases: (1) fixed sediment mass with constant probabilities of erosion and preservation; (2) fixed sediment mass with erosion and preservation probabilities that vary with geologic age; and (3) growing sediment mass with constant probabilities of erosion, preservation, and removal from the sedimentary cycle. For geologically long periods of time, the stochastic models can be transformed into such models of sediment preservation as the exponential or compound decay of a fixed sediment mass and a continuous growth of the sediment mass. Several of the statistical distributions arising out of the stochastic models- the geometric, exponential, compound decay, and inverse hypergeometric-produce mass-age distribution curves for the Phanerozoic and Late Proterozoic sediments that agree reasonably well with the actual masses reported in the literature. A general characteristic of the stochastic models is that for any mass-age distribution of sediments when the mass decreases with an increasing geologic age, there always exist sets of preservation and erosion probabilities that describe the process of sediment aging.